Optimizing control feedforward

Optimal feedforward control strategies can be treated within the framework of the LQP (49). 

As shown in the above works, an optimal feedback/feedforward controller can be derived as an analytical function of the numerator and denominator polynomials of Gp(B) and Gn(B). No iteration or integration is required to generate the feedback law, as a consequence of the one step ahead criterion. Shinnar and Palmor (52) have also clearly demonstrated how dead time compensation (discrete time Smith predictor) arises naturally out of the minimum variance controller. These minimum variance techniques can also be extended to multi-variable systems, as shown by MacGregor (51). 

Using the transfer function concept, Koppel (1967) derived the optimal control policy for a heat exchanger system described by hyperbolic partial differential equations using the lumped system approach. Koppel and Shih (1968) also presented a feedback interior control for a class of hyperbolic differential equations with distributed control. In an earlier paper Koppel e/ al. (1968) discussed the necessary conditions for the system with linear hyperbolic partial differential equations having a control which is independent of spatial coordinates. The optimal feedback-feedforward control law for linear hyperbolic systems, whose dynamical response to input variations is characterized by an initial pure time delay, was derived by Denn... 

Chapter 21. Chapter 7 in Shinskey [Ref. 3] is again an excellent reference for the practical considerations guiding the design of feedforward and ratio control systems. It also discusses the use of feedforward schemes for optimizing control of processing systems. Good tutorial references are the books by Smith [Ref. 2], Murrill [Ref. 8], and Luyben [Ref. 9]. The last one has a simple but instructive example on the nonlinear feedforward control of a CSTR. 

A different type of closed-loop control is feedforward control, in which optimal controls are explicitly obtained in advance from the inputs in conjunction with the mathematical model of a system. As shown in the above figure, feedforward controls are applied to the system without having to wait for the system state the inputs and controls would later generate. 

Use override control to achieve variable control structures to handle constraints and valve position control to achieve self-optimizing control in a simple and inexpensive way. Use ratio (feedforward) control to improve load rejection. 

Some plants have been using computer control for 20 years. Control systems in industrial use typically consist of individual feedback and feedforward loops. Horst and Enochs [Engineering h- Mining]., 181(6), 69-171 (1980)] reported that installation of single-variable automatic controls improved performance of 20 mineral processing plants by 2 to 10 percent. But interactions among the processes make it difficult for independent controllers to control the circuit optimally. 

Holena, M., Baerns, M., Feedforward neural networks in catalysis, a tool for the approximation of the dependency of yield on catalyst composition, and for knowledge extraction, Catal. Today 2003, 81, 485-494. Serra, J. M., Corma, A., Argente, E., Valero, S., Botti, V., Neuronal networks for modeling of kinetic reaction data applicable to catalyst scale up and process control and optimization in the frame of combinatorial catalysis, Appl. Catal. A 2003, 254, 133-145. 

The design, optimization, and control of the EMR for the decolorization of Orange II require the implementation of a control system. Two control systems were developed (a) a feedforward system based on the knowledge of kinetics and reactor hydraulics and (b) a feedback system based on the concentration of DO into the reactor, which was observed to be a main variable that provides extensive information about the development of the process. 

We showed through nonlinear dynamic simulations how the process reacts to various disturbances and changes in operating conditions. We have not shown any attempts to optimize process performance, to improve the process design, or to apply any advanced control techniques (model-based, nonlinear, feedforward, valve-position, etc.). These would be the natural next steps after the base-level regulatory control system had been developed to keep the process at a stable desired operating point. 

The variables indicated by an asterisk ( ) were assigned a priori. The feedforward (FF) trim controller gain is dimensionless as both the input and the output are ratios of flows. The CSTR controller gains are in m /h reagent per m /h acid at maximum flow per pH. Some of the tuning parameters were on bounds, but the associated Lagrange multipliers did not indicate a significant incentive to rerun the optimization. 

MFC control approach shows its incentives over the classical decentralized FI control due to the intrinsic capability of counteracting interactions between controlled variables, the use of future process behaviour predictions for computing the control actions, the straightforward implementation of the combined feedforward-fedback control setup, the capability of systematic constraints handling and its optimal feature, all as a result of directly involving the process model in the MFC control law. 

The essential step in the LQG benchmark is the calculation of various control laws for different values of A and prediction (P) and control (M) horizons (P = M). This is a case study for a special type of MPC (unconstrained, no feedforward) and a special parameter set (M = P) to find the optimal value of the cost function and an optimal controller parameter set. Using the same information (plant and disturbance model, covariance matrices of noise and disturbances), studies can be conducted for any t3q>e of MPC and the influence of any parameter can be examined. These studies... 

From previous experimental data we know how the optimal fuel/air ratio changes with air temperature for maximum efficiency. Therefore, to maintain the ratio continuously at its optimal value despite any changes in the air temperature, we can use a programmed adaptive control system. Such a system is shown in Figure 22.3b. It measures the temperature of the air (auxiliary measurement) and adjusts the value of the fuel/air ratio. Notice again that the ratio adjustment mechanism is like feedforward compensation. 

How can we use the tremendous computational power of a computer to implement some advanced notions of process control, such as feedforward, adaptive, inferential, optimizing, and so on ... 

The constructive method, which is considered as a major breakthrough in control theory, was developed in the last decade. As it stands, the method is intended for feedback control design, and its application to the batch motion case requires the nominal output to be tracked and a suitable definition of finite-time batch motion stability. In a more applied eontext, the inverse optimality idea has been applied to design the nominal motion of homo [11] and copolymer [12] reactor, obtaining results that are similar to the ones drawn from direct optimization [4]. The motion was obtained from the recursive application of the process dynamical inverse [13], and the inverse yielded a nonlinear SF controller [9, 10] that was in turn used to specify a conventional feedforward-feedback industrial control scheme. However, the issues of motion stability and systematized search were not formally addressed. 

An important observation is that any control program may be followed, even one that would cause the process gain dc/dm to change sign. Hence feedforward is the logical means to achieve optimizing (steady-state adaptive) control. This has already been demonstrated in Chap. 6. 

Write the equation for the feedforward system which controls exit-gas composition y as it leaves the absorber described under the section on optimizing programs. How does this differ from the optimizing program solved in the example ... 

Absorption is not a refining operation and is rarely the last operation conducted on a product. Consequently, close control of the concentration of either effluent stream is not paramount, and on-line analyzers are not often used. More importance is placed on minimizing losses (such as Vy) or total operating costs, for which the simple optimizing feedforward system was designed at the close of Chap. 8. In that example, as in the control equation (12.8), maintenance of a designated ratio of L/F applies. 

Once a distillation column or train for a continuous chemical process has been designed and built, the three best opportunities for profitable operation via process control are usually (1) maximum-capacity operation if the plant is production limited, (2) minimum-cost operation if the plant is market limited, and (3) increased annual availability (sometimes called utility). The last of these is greatly aided by constraint controls, commonly called overrides, to keep the plant operating safely and smoothly when it mi t otherwise be shut down by interlodu or operator decision. Maximum-capacity or minimum-cost operation is facilitated by the use of on-line models, usually implemented by a digital computer. Fxmctionally these will be, in most cases, sophisticated feedforward compensators, or constraint controls. With these two limited exceptions, optimization is not considered in this book. Since the on-line models to be employed require calibration, some degree of on-line identification is highly desirable. 

In Chapter 12 we proposed a particular control-loop stmeture that incorporates overrides and antireset windup. It also accommodates feedforward compensation and advanced control techniques without interfering with either normal reset or antireset windup. We also suggested that decouplers could be designed to compensate for interactions in e same way that feedforward compensators are designed. The technique here leads to stable, noninteracting control, but not necessarily to optimum control. Modem control theory, with its more sophisticated approaches to multivariable control, sometimes reqtiires some interaction for optimality. 

Once a conceptual control structure has been developed and the plant has been decomposed into subsystems, the control design procedure reverts to a traditional bottom-up approach. However, there are good reasons to treat the different control activities in a multilevel hierarchy, as shown in Fig. H.l. The first task in Step III is to identify the essential controllers, those that are absolutely required. The safety and regulatory levels in Fig. H.l enable safe and stable operation of the plant. The advanced control functions are handled at Level 3 and keep the controlled variables close to their optimum set points through standard methods such as cascade, ratio, feedforward, and multivariable control. Level 4 in Fig. H.1 considers the real-time optimization of the process operations. The purpose of control at this level is to choose operating conditions that meet overall objectives in an economically optimum fashion. 

Ruegsegger, S., Wagner, A., Freudenberg, J., Grimard, D. Optimal feedforward recipe adjustment for CD control in semiconductor patterning. In Characterization and Metrology for ULSI Technology 1998 International Confoence, pp. 753—577. The American Instimte of Physics (1998). ISBN 1-56396-753-7... 

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